Double Marginalization Q The 2 Suppose that the market demand for a product is given by P = 240 marginal cost of manufacturing the product is $30, the marginal cost of selling the good is $10

A) When a single product is manufacturing and selling product the the total marginal cost will be equal to $40.

Now,

P=240-Q/2

R=P*Q

R=240Q-Q²/2

MR=dR/dQ

MR=240-Q

At profit maximizing quantity MC=MR

240-Q=40

Q=200 and

P=240-200/2

P=$140

Profit=TR-TC

Profit=200*140-200*40=$20,000.

B.i)

Let the price for manufacturer be Pm and the price for retailer be P.

The marginal profit for retailer will be P-Pm-10 and quantity sold will be Q=480-2P

The profit for retailer would be (P-Pm-10)(480-2P)

PR=480P-480Pm-4,800-2P²+2PmP+20P

For profit maximization the derivative of PR with respect to P will be zero

0=500-4P+2Pm

Pm=2P-250

or

P=Pm/2+125

ii)

The marginal profit for manufacturer will be Pm-30

The profit for retailer would be (Pm-30)(240-Pm)

PR=240Pm-7,200-Pm²+30Pm

For profit maximization the derivative of PR with respect to P will be zero

0=270-2Pm

Pm=$135

or

P=135/2+125=$192.5

The profit for manufacturing firm is

Profit=(Pm-$30)*Q=($135-$30)*200=$21,000

The profit for retailer is

Profit=(P-Pm-$10)*Q=($192.5-$135-$10)*200=$9,500